Thesis (doctoral) - Radboud Universiteit, Nijmegen, 2010. / Includes index.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 149-160).

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

<p>WKB theory provides a plausible link between classical mechanics and quantum mechanics in its semi-classical limit. Connecting the WKB wave function across the turning points in a quantum well, leads to the WKB quantization condition. In this work, I focus on some improvements and recent developments related to the WKB quantization condition. First I discuss how the combination of super-symmetric quantum mechanics and WKB, gives the SWKB quantization condition which is exact for a large class of potentials called shape invariant potentials. Next I turn to the fact that there is always a probability of refection when the potential is not constant and the phase of the wave function should account for this refection. WKB theory ignores refection except at turning points. I explain the work of Friedrich and Trost who showed that by including the correct "refection phase" at a turning point, the WKB quantization condition can be made to give exact bound state energies. Next I discuss the work of Cao and collaborators which takes refection of the wave function into account everywhere. We show that Cao's method provides a way to compute the F-T refection phase. Finally I discuss a paper of Fabre and Guery-Odelin who used the exponential potential to study the accuracy of WKB. In their results the accuracy deteriorates as the energy increases, which is inconsistent with Bohr's correspondence principle. Using the Friedrich and Trost method, we resolved this problem.</p> / Master of Science (MSc)

Quantum information processing has the potential of implementing faster algorithms for numerous problems, communicating with more secure channels, and performing higher precision sensing compared to classical methods. Recent experimental technology advancement has brought us a promising future of harnessing such quantum advantage. Yet, quantum engineering entails wise control and strategy under the current noisy intermediate-scale quantum era. Developing robust and efficient approaches to manipulating quantum systems based on constrained and limited resources is imperative. This dissertation focuses on two major topics theoretically. In the first part, this work present how to conceive robust quantum control on matter-based qubits with a geometric approach. We have proposed the method of designing noise robust control pulses suitable for practical devices by combining spatial curves, filter functions, and machine learning. In the second part, this work stresses the topic of photonic multipartite entangled graph states. An improved protocol of generating arbitrary graph states is introduced. We show that one can efficiently find the deterministic photon emission circuit with minimal overhead on the number of quantum emitters. / Doctor of Philosophy / As classical information technology has revolutionized our modern world, theoretically, quantum information technology outperforms its classical counterpart and has the potential to achieve further progress. Utilizing the non-classical features unique to quantum physics, one can build quantum computers capable of accelerating data searching, breaking most current cryptographic systems, simulating molecular-level dynamics, and enhancing artificial intelligence. Furthermore, one can use the entangled quantum resource to establish secure communication or increase the capacity of the classical communication channel. Although numerous applications may reshape our daily life, industry, and scientific research, the mastery of quantum information technology is still challenging since quantum systems are more susceptible to noise than classical systems. Unlike classical signal processing, reading out an unknown quantum state will irreversibly change the state, while copying an unknown quantum state is strictly infeasible. Therefore, detecting and correcting errors from quantum data can be tricky. Depending on different platforms, establishing a complicated quantum network can also be constrained by the near-term noisy device. Mainly, what this work attempts to innovate are the previous results on quantum dynamical control pulse design and the protocol of entangling photons. For the former, the goal of this work is to develop control pulses that can decouple coherent noise in the quantum computer when manipulating the quantum information. This work combines the mathematical framework of spatial curve quantum control with filter functions and machine learning to yield new outcomes. The flexibility of this framework enables us to give neat mathematical analysis and obtain satisfying control pulses design for physical implementations through numerical experiments. For the latter, this work studies a promising scheme of deterministically producing an entangling photonic quantum network, where quantum emitters are treated as the media to build up quantum non-locality. Achieving this emission process in the real world is desirable for distributing entangled quantum resources and realizing measurement-based quantum computation. In this case, we analyze the emitter overhead needed to generate an entangling photonic resource state, specifically when sending photons back for interactions is inaccessible. At last, we propose an efficient algorithm for producing the generation protocol along with several practical examples whose overheads on quantum emitters number are strictly optimized.

This dissertation consists of three sections. In the first section, we discuss the generation of arbitrary two-qubit entangled states and present three generation methods. The first method is based on the interaction of an atom with classical and quantized cavity fields. The second method is based on the interaction of two coupled two-level atoms with a laser field. In the last method, we use two spin-1/2 systems which interact with a tuned radio frequency pulse. Using those methods we have generated two qubit arbitrary entangled states which is widely used in quantum computing and quantum information. In the second section, we discuss a possible experimental implementation of quantum walk which is based on the passage of an atom through a high-Q cavity. The chirality is determined by the atomic states and the displacement is characterized by the photon number inside the cavity. Our scheme makes quantum walk possible in a cavity QED system and the results could be widely used on quantum computer. In the last section, we investigate the properties of teleporting an arbitrary superposition of entangled Dicke states of any number of atoms (qubits) between two distant cavities. We also studied teleporting continuous variables of an optical field. Teleportation of Dicke states relies on adiabatic passage using multiatom dark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate the protocol of quantum teleportation of arbitrary input optical field states in the density matrix form, and established the relation between the P-function of the input and output states. We then present a condition involving squeeze parameter and detection efficiency under which the P-function of the output state becomes the Q function of the input state such that any nonclassical features in the input state will be eliminated in the teleported state. Based on the research in this section we have made it possible of arbitrary atomic Dicke states teleportation from one cavity to another, and this teleortation will play an essential role in quantum communication. Since quantum properties is so important in quantum communication, the condition we give in this section to distinguish classical and quantum teleportation is also important.

No description available.

Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Chapman, Michael; Committee Member: Citrin, David; Committee Member: Kennedy, T. A. Brian; Committee Member: Kuzmich, Alexander; Committee Member: Raman, Chandra. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph.D.) - University of St Andrews, April 2009.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008. / Minqiang Li, Committee Member ; Constantine Yannouleas, Committee Member ; Michael Pustilnik, Committee Member ; Mei-Yin Chou, Committee Member ; Uzi Landman, Committee Member.